I there a way to move multiple vertices preserving a straight line
I can´t see in which axis you did the capture but for Option A I will assume it is a TOP VIEW so:
Select both of these RED circled vertex, now press S, SHIFT and DRAG to the RIGHT to scale them and make them align at SCALE 0 for both vertex.

If this is not what you expected, you can select and SLIDE the vertex you are interested by selecting the vertex and then press GG to move it

If this is still not what you expected, then select the vertex you want to align parpendicularly. Press X, D. Your vertex will be removed. Now, use the KNIFE (K) to make a clean cut from the appointed verted like in this graphic marked with the BLUE line as option 2.


Thanks for voting me up on this question or selecting it as your answer.

BFCT_Schiller